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arXiv · 2404.05416

Geometry of infinite dimensional Cartan Developments

Johanna Michor·Peter W. Michor
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Abstract

The Cartan development takes a Lie algebra valued 1-form satisfying the Maurer-Cartan equation on a simply connected manifold $M$ to a smooth mapping from $M$ into the Lie group. In this paper this is generalized to infinite dimensional $M$ for infinite dimensional regular Lie groups. The Cartan development is viewed as a generalization of the evolution map of a regular Lie group. The tangent mapping of a Cartan development is identified as another Cartan development.

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Johanna Michor, Peter W. Michor. 2024-04-08. Geometry of infinite dimensional Cartan Developments. https://arxiv.org/abs/2404.05416

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